Komal can do a work in $51$ days. Bimal is $50\%$ more efficient than Komal in doing the work. In how many days Bimal will do that work?

Let the efficiency of Komal be $E_K$ and the efficiency of Bimal be $E_B$.
Since Bimal is $50\%$ more efficient than Komal:

$$E_B=E_K+50\%\text{ of }{E}_K=1.5E_K=\frac{3}{2}{E}_K$$

The amount of time taken to complete a certain constant amount of work is inversely proportional to the efficiency:

$$\text{Efficiency}\times \text{Time}=\text{Total Work}$$

$$E_K\times 51=E_B\times T_B$$

Substituting the value of $E_B$:

$$E_K\times 51=\left(\frac{3}{2}{E}_K\right)\times T_B$$

$$51=\frac{3}{2}\times T_B$$

$$T_B=51\times \frac{2}{3}$$

$$T_B=17\times 2=34\text{ days}$$